Does AS size determine degree in as topology?

In a recent and much celebrated paper, Faloutsos et al. [6] found that the inter Autonomous System (AS) topology exhibits a power-law degree distribution . This result was quite unexpected in the networking community , and stirred significant interest in exploring the possible causes of this phenomenon. The work of Barabasi et al. [2], and its application to network topology generation in the work of Medina et al. [9], have explored a promising class of models that yield strict power-law degree distributions. These models, which we will refer to collectively as the B-A model, describe the detaile d dynamics of the network growth process, modeling the way in which connections are made between ASs. There are two simple connectivity rules that define the evolution of AS connectivity over time : incremental growth where a new AS connects to existing ASs, and preferential connectivity where the likelihood of connecting to an AS is proportional to the vertex outdegree of the target AS. These simple rules, which are similar to the classical "rich get richer" model originally proposed by Simon [12], lead to power-law degree distributions.